Moment Alignment: Unifying Gradient and Hessian Matching for Domain Generalization

Domain generalization (DG) seeks to develop models that generalize well to unseen target domains, addressing the prevalent issue of distribution shifts in real-world applications. One line of research in DG focuses on aligning domain-level gradients and Hessians to enhance generalization. However, existing methods are computationally inefficient and the underlying principles of these approaches are not well understood. In this paper, we develop the theory of moment alignment for DG. Grounded in \textit{transfer measure}, a principled framework for quantifying generalizability between two domains, we first extend the definition of transfer measure to domain generalization that includes multiple source domains and establish a target error bound. Then, we prove that aligning derivatives across domains improves transfer measure both when the feature extractor induces an invariant optimal predictor across domains and when it does not. Notably, moment alignment provides a unifying understanding of Invariant Risk Minimization, gradient matching, and Hessian matching, three previously disconnected approaches to DG. We further connect feature moments and derivatives of the classifier head, and establish the duality between feature learning and classifier fitting. Building upon our theory, we introduce \textbf{C}losed-Form \textbf{M}oment \textbf{A}lignment (CMA), a novel DG algorithm that aligns domain-level gradients and Hessians in closed-form. Our method overcomes the computational inefficiencies of existing gradient and Hessian-based techniques by eliminating the need for repeated backpropagation or sampling-based Hessian estimation. We validate the efficacy of our approach through two sets of experiments: linear probing and full fine-tuning. CMA demonstrates superior performance in both settings compared to Empirical Risk Minimization and state-of-the-art algorithms.

MiCRo: Mixture Modeling and Context-aware Routing for Personalized Preference Learning

Reward modeling is a key step in building safe foundation models when applying reinforcement learning from human feedback (RLHF) to align Large Language Models (LLMs). However, reward modeling based on the Bradley-Terry (BT) model assumes a global reward function, failing to capture the inherently diverse and heterogeneous human preferences. Hence, such oversimplification limits LLMs from supporting personalization and pluralistic alignment. Theoretically, we show that when human preferences follow a mixture distribution of diverse subgroups, a single BT model has an irreducible error. While existing solutions, such as multi-objective learning with fine-grained annotations, help address this issue, they are costly and constrained by predefined attributes, failing to fully capture the richness of human values. In this work, we introduce MiCRo, a two-stage framework that enhances personalized preference learning by leveraging large-scale binary preference datasets without requiring explicit fine-grained annotations. In the first stage, MiCRo introduces context-aware mixture modeling approach to capture diverse human preferences. In the second stage, MiCRo integrates an online routing strategy that dynamically adapts mixture weights based on specific context to resolve ambiguity, allowing for efficient and scalable preference adaptation with minimal additional supervision. Experiments on multiple preference datasets demonstrate that MiCRo effectively captures diverse human preferences and significantly improves downstream personalization.

Taming Hyperparameter Sensitivity in Data Attribution: Practical Selection Without Costly Retraining

Data attribution methods, which quantify the influence of individual training data points on a machine learning model, have gained increasing popularity in data-centric applications in modern AI. Despite a recent surge of new methods developed in this space, the impact of hyperparameter tuning in these methods remains under-explored. In this work, we present the first large-scale empirical study to understand the hyperparameter sensitivity of common data attribution methods. Our results show that most methods are indeed sensitive to certain key hyperparameters. However, unlike typical machine learning algorithms -- whose hyperparameters can be tuned using computationally-cheap validation metrics -- evaluating data attribution performance often requires retraining models on subsets of training data, making such metrics prohibitively costly for hyperparameter tuning. This poses a critical open challenge for the practical application of data attribution methods. To address this challenge, we advocate for better theoretical understandings of hyperparameter behavior to inform efficient tuning strategies. As a case study, we provide a theoretical analysis of the regularization term that is critical in many variants of influence function methods. Building on this analysis, we propose a lightweight procedure for selecting the regularization value without model retraining, and validate its effectiveness across a range of standard data attribution benchmarks. Overall, our study identifies a fundamental yet overlooked challenge in the practical application of data attribution, and highlights the importance of careful discussion on hyperparameter selection in future method development.

GraSS: Scalable Influence Function with Sparse Gradient Compression

Gradient-based data attribution methods, such as influence functions, are critical for understanding the impact of individual training samples without requiring repeated model retraining. However, their scalability is often limited by the high computational and memory costs associated with per-sample gradient computation. In this work, we propose GraSS, a novel gradient compression algorithm and its variants FactGraSS for linear layers specifically, that explicitly leverage the inherent sparsity of per-sample gradients to achieve sub-linear space and time complexity. Extensive experiments demonstrate the effectiveness of our approach, achieving substantial speedups while preserving data influence fidelity. In particular, FactGraSS achieves up to 165% faster throughput on billion-scale models compared to the previous state-of-the-art baselines. Our code is publicly available at https://github.com/TRAIS-Lab/GraSS.

A Snapshot of Influence: A Local Data Attribution Framework for Online Reinforcement Learning

Online reinforcement learning (RL) excels in complex, safety-critical domains, yet it faces challenges such as sample inefficiency, training instability, and a lack of interpretability. Data attribution offers a principled way to trace model behavior back to individual training samples. However, in online RL, each training sample not only drives policy updates but also influences future data collection, violating the fixed dataset assumption in existing attribution methods. In this paper, we initiate the study of data attribution for online RL, focusing on the widely used Proximal Policy Optimization (PPO) algorithm. We start by establishing a local attribution framework, interpreting model checkpoints with respect to the records in the recent training buffer. We design two target functions, capturing agent action and cumulative return respectively, and measure each record's contribution through gradient similarity between its training loss and these targets. We demonstrate the power of this framework through three concrete applications: diagnosis of learning, temporal analysis of behavior formation, and targeted intervention during training. Leveraging this framework, we further propose an algorithm, iterative influence-based filtering (IIF), for online RL training that iteratively performs experience filtering to refine policy updates. Across standard RL benchmarks (classic control, navigation, locomotion) to RLHF for large language models, IIF reduces sample complexity, speeds up training, and achieves higher returns. Overall, these results advance interpretability, efficiency, and effectiveness of online RL.

Not All Correct Answers Are Equal: Why Your Distillation Source Matters

Distillation has emerged as a practical and effective approach to enhance the reasoning capabilities of open-source language models. In this work, we conduct a large-scale empirical study on reasoning data distillation by collecting verified outputs from three state-of-the-art teacher models-AM-Thinking-v1, Qwen3-235B-A22B, and DeepSeek-R1-on a shared corpus of 1.89 million queries. We construct three parallel datasets and analyze their distributions, revealing that AM-Thinking-v1-distilled data exhibits greater token length diversity and lower perplexity. Student models trained on each dataset are evaluated on reasoning benchmarks including AIME2024, AIME2025, MATH500, and LiveCodeBench. The AM-based model consistently achieves the best performance (e.g., 84.3 on AIME2024, 72.2 on AIME2025, 98.4 on MATH500, and 65.9 on LiveCodeBench) and demonstrates adaptive output behavior-producing longer responses for harder tasks and shorter ones for simpler tasks. These findings highlight the value of high-quality, verified reasoning traces. We release the AM-Thinking-v1 and Qwen3-235B-A22B distilled datasets to support future research on open and high-performing reasoning-oriented language models. The datasets are publicly available on Hugging Face\footnote{Datasets are available on Hugging Face: \href{https://huggingface.co/datasets/a-m-team/AM-Thinking-v1-Distilled}{AM-Thinking-v1-Distilled}, \href{https://huggingface.co/datasets/a-m-team/AM-Qwen3-Distilled}{AM-Qwen3-Distilled}.}.

SSR: Enhancing Depth Perception in Vision-Language Models via Rationale-Guided Spatial Reasoning

Despite impressive advancements in Visual-Language Models (VLMs) for multi-modal tasks, their reliance on RGB inputs limits precise spatial understanding. Existing methods for integrating spatial cues, such as point clouds or depth, either require specialized sensors or fail to effectively exploit depth information for higher-order reasoning. To this end, we propose a novel Spatial Sense and Reasoning method, dubbed SSR, a novel framework that transforms raw depth data into structured, interpretable textual rationales. These textual rationales serve as meaningful intermediate representations to significantly enhance spatial reasoning capabilities. Additionally, we leverage knowledge distillation to compress the generated rationales into compact latent embeddings, which facilitate resource-efficient and plug-and-play integration into existing VLMs without retraining. To enable comprehensive evaluation, we introduce a new dataset named SSR-CoT, a million-scale visual-language reasoning dataset enriched with intermediate spatial reasoning annotations, and present SSRBench, a comprehensive multi-task benchmark. Extensive experiments on multiple benchmarks demonstrate SSR substantially improves depth utilization and enhances spatial reasoning, thereby advancing VLMs toward more human-like multi-modal understanding. Our project page is at https://yliu-cs.github.io/SSR.

MergeBench: A Benchmark for Merging Domain-Specialized LLMs

Model merging provides a scalable alternative to multi-task training by combining specialized finetuned models through parameter arithmetic, enabling efficient deployment without the need for joint training or access to all task data. While recent methods have shown promise, existing evaluations are limited in both model scale and task diversity, leaving open questions about their applicability to large, domain-specialized LLMs. To tackle the challenges, we introduce MergeBench, a comprehensive evaluation suite designed to assess model merging at scale. MergeBench builds on state-of-the-art open-source language models, including Llama and Gemma families at 2B to 9B scales, and covers five key domains: instruction following, mathematics, multilingual understanding, coding and safety. We standardize finetuning and evaluation protocols, and assess eight representative merging methods across multi-task performance, forgetting and runtime efficiency. Based on extensive experiments, we provide practical guidelines for algorithm selection and share insights showing that model merging tends to perform better on stronger base models, with techniques such as merging coefficient tuning and sparsification improving knowledge retention. However, several challenges remain, including the computational cost on large models, the gap for in-domain performance compared to multi-task models, and the underexplored role of model merging in standard LLM training pipelines. We hope MergeBench provides a foundation for future research to advance the understanding and practical application of model merging. We open source our code at \href{https://github.com/uiuctml/MergeBench}{https://github.com/uiuctml/MergeBench}.

Unveiling the Potential of Vision-Language-Action Models with Open-Ended Multimodal Instructions

Vision-Language-Action (VLA) models have recently become highly prominent in the field of robotics. Leveraging vision-language foundation models trained on large-scale internet data, the VLA model can generate robotic actions directly from visual observations and human instructions through a single end-to-end neural network. Despite their effectiveness, current VLA models usually accept only one form of human prompting, language instructions, which may constrain their applicability in open-ended human-robot interactions. For example, a user might expect the robot to retrieve an object shown in an image, follow an instruction written on the whiteboard, or imitate a behavior demonstrated in a video, rather than relying solely on language-based descriptions. To address this gap, we introduce OE-VLA, which explores the potential of VLA models for open-ended multimodal instructions. Extensive results demonstrate that our OE-VLA not only achieves comparable performance to traditional VLA models with linguistic input but also delivers impressive results across four additional categories of open-ended tasks. The proposed methodology could significantly expand the applications of VLA models across various everyday scenarios and facilitate human-robot interaction.

AM-Thinking-v1: Advancing the Frontier of Reasoning at 32B Scale

We present AM-Thinking-v1, a 32B dense language model that advances the frontier of reasoning, embodying the collaborative spirit of open-source innovation. Outperforming DeepSeek-R1 and rivaling leading Mixture-of-Experts (MoE) models like Qwen3-235B-A22B and Seed1.5-Thinking, AM-Thinking-v1 achieves impressive scores of 85.3 on AIME 2024, 74.4 on AIME 2025, and 70.3 on LiveCodeBench, showcasing state-of-the-art mathematical and coding capabilities among open-source models of similar scale. Built entirely from the open-source Qwen2.5-32B base model and publicly available queries, AM-Thinking-v1 leverages a meticulously crafted post-training pipeline - combining supervised fine-tuning and reinforcement learning - to deliver exceptional reasoning capabilities. This work demonstrates that the open-source community can achieve high performance at the 32B scale, a practical sweet spot for deployment and fine-tuning. By striking a balance between top-tier performance and real-world usability, we hope AM-Thinking-v1 inspires further collaborative efforts to harness mid-scale models, pushing reasoning boundaries while keeping accessibility at the core of innovation. We have open-sourced our model on \href{https://huggingface.co/a-m-team/AM-Thinking-v1}{Hugging Face}.